Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

269×

body

valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	36	7
2	48	7
3	66	7
4	72	7
5	72	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.7b	(- (* b c) (* a d))
25.6b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-/r` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 55

Calls

3 calls:

2.0ms	(+ (* c c) (* d d))
2.0ms	(- (* b c) (* a d))
10.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series155.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* c c) (* d d))
41.0ms	(- (* b c) (* a d))
88.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify38.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	292	541
1	1273	493
2	5002	491

prune183.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 25.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* b c) (* a d))
17.3b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
29.5b	(sqrt (+ (* c c) (* d d)))
29.5b	(sqrt (+ (* c c) (* d d)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 86

Calls

4 calls:

2.0ms	(- (* b c) (* a d))
10.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
4.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series230.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (* b c) (* a d))
114.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
38.0ms	(sqrt (+ (* c c) (* d d)))
36.0ms	(sqrt (+ (* c c) (* d d)))

simplify98.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	304	910
1	990	857
2	3354	845
3	5001	845

prune277.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* b c) (* a d))
17.3b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
29.5b	(sqrt (+ (* c c) (* d d)))
29.5b	(sqrt (+ (* c c) (* d d)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 86

Calls

4 calls:

2.0ms	(- (* b c) (* a d))
10.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
3.0ms	(sqrt (+ (* c c) (* d d)))
3.0ms	(sqrt (+ (* c c) (* d d)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (* b c) (* a d))
111.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
35.0ms	(sqrt (+ (* c c) (* d d)))
39.0ms	(sqrt (+ (* c c) (* d d)))

simplify96.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	304	910
1	990	857
2	3354	845
3	5001	845

prune289.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 22.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.6b	(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
0.7b	(- (* b c) (* a d))
25.1b	(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
8×	`div-exp` `add-log-exp`
6×	`flip3--` `flip--` `div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv`
2×	`rec-exp` `frac-2neg` `flip3-+` `1-exp` `clear-num` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `pow-flip` `diff-log` `sum-log` `inv-pow`

Counts

4 → 138

Calls

4 calls:

2.0ms	(+ (* c c) (* d d))
13.0ms	(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
2.0ms	(- (* b c) (* a d))
11.0ms	(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* c c) (* d d))
136.0ms	(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
42.0ms	(- (* b c) (* a d))
53.0ms	(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

simplify65.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	516	1825
1	2545	1663
2	5001	1577

prune270.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 22.9b

regimes164.0ms

Accuracy

0% (3.1b remaining)

Error of 26.5b against oracle of 23.3b and baseline of 26.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	13
1	16	13

end0.0ms

sample514.0ms

Algorithm

intervals

Results

305.0ms

8464×

body

valid